Stats Unit 2 MC
A researcher studying a specific type of tree creates a least-squares regression line for relating the height and the diameter, both in meters, of a fully grown tree. The results are shown in the following computer output. Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree? A. 30 B. 5 C. 4 D. 2.5 E. 130
A
Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Partial-cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, in squirrels per plot, 2 to 4 years after partial-cut harvesting, and the percent of trees that were harvested in each of 11 forests. Which of the following is the best description of the relationship displayed in the scatterplot? A Negative, linear, and strong B Positive, linear, and weak C Negative, nonlinear, and strong D Positive, nonlinear, and weak E Positive, nonlinear, and strong
A
The following data were collected from a random sample of people on their favorite types of leisure activities and their age. The results are shown in the two-way table below. What proportion of the people aged 7 to 18 years gave watching television as their favorite type of leisure activity? A 300/2,200 B 200/900 C 100/1300 D 640/3500 E 300/640
A
A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. What was the value of the correlation coefficient? A 0.64 B 0.60 C 0.40 D 0.36 E 0.13
B
A set of bivariate data was used to create a least-squares regression line. Which of the following is minimized by the line? A The sum of the residuals B The sum of the squared residuals C The sum of the absolute values of the residuals D The influence of outliers E The slope
B
Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. The least-squares regression line produced from a random sample is Milkˆ=40.8−1.1(Age)Milk^=40.8−1.1(Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years? A A cow of 5 years is predicted to produce 5.5 fewer gallons per week. B A cow of 5 years is predicted to produce 5.5 more gallons per week. C A cow of 5 years is predicted to produce 1.1 fewer gallons per week. D A cow of 5 years is predicted to produce 1.1 more gallons per week. E A cow of 5 years and a cow of 10 years are both predicted to produce 40.8 gallons per week.
B
A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and height was computed to be 0. What does this correlation suggest about the relationship between the time and height? A There is no relationship between time and height. B There is no linear relationship between time and height. C The distance the ball traveled upward is the same as the distance the ball traveled downward. D The correlation suggests that there is measurement or calculation error. E The correlation suggests that more measurements should be taken to better understand the relationship.
B There is no linear relationship between time and height.
A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation? A 0.59 months per pound B 0.59 pounds per month C 0.59 D 0.59 months times pounds E 0.59 month pounds
C
A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant? A The relationship is linear because the correlation is positive. B The relationship is not linear because the correlation is positive. C The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant. D The parties with a larger number of customers are associated with the shorter times elapsed until the party left the restaurant. E There is no relationship between the number of customers in a party at a table in the restaurant and the time required until the party left the restaurant.
C
A split ticket is a voting pattern in which a voter casts votes for candidates from more than one political party. In a recent study, 1,000 men and women were asked whether they voted a split ticket in the last election. The totals are shown in the following table. What value of a would indicate no association between gender and voting pattern for the people in the sample? A. 300 B. 400 C. 480 D. 500 E. 800
C
Researchers observed the grouping behavior of deer in different regions. The following scatterplot shows data collected on the size of the group and the percent of the region that was woodland. The relationship between group size and percent woodland appears to be negative and nonlinear. Which of the following statements explains such a relationship? A As the percent of woodland increases, the number of deer observed in a group decreases at a fairly constant rate. B As the percent of woodland increases, the number of deer observed in a group increases at a fairly constant rate. C As the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly. D As the percent of woodland increases, the number of deer observed in a group increases quickly at first and then more slowly. E As the percent of woodland increases, the number of deer observed in a group remains fairly constant.
C
The relationship between carbon dioxide emissions and fuel efficiency of a certain car can be modeled by the least-squares regression equation ln(yˆ)=7−0.045x, where x represents the fuel efficiency, in miles per gallon, and yˆ represents the predicted carbon dioxide emissions, in grams per mile . Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon? A. 1.8 B. 6.1 C. 446 D. 2,697 E. 1,250,000
C. 446
For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long? A Yes, because 3 inches falls above the maximum value of lengths in the sample. B Yes, because the regression equation is based on a random sample. C Yes, because the association between length and weight is positive. D No, because 3 inches falls above the maximum value of lengths in the sample. E No, because there may not be any 3-inch fish of this species in the pond.
D
The following bar chart displays the relative frequency of responses of students, by grade level, when asked, "Do you volunteer in a community-service activity?" Which of the following statements is not supported by the bar chart? A. More than 60% of both tenth-grade and eleventh-grade students responded yes. B. Twelfth-grade students had the least percentage of students respond yes. C. Less than 40% of tenth-grade students responded no. D. The number of tenth-grade students who responded yes was greater than the number of ninth-grade students who responded yes. E. The percentage of eleventh-grade students who responded no was less than the percentage of ninth-grade students who responded no.
D
Which of the following is the best description of a positive association between two variables? A The values will create a line when graphed on a scatterplot. B The values will create a line with positive slope when graphed on a scatterplot. C As the value of one of the variables increases, the value of the other variable tends to decrease. D As the value of one of the variables increases, the value of the other variable tends to increase. E All values of both variables are positive.
D
An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot? A There should be a positive, linear association in the residual plot. B There should be a negative, linear association in the residual plot. C All of the points must have residuals of 0. D There should be no pattern in the residual plot. E The residuals should have a small amount of variability for low values of the predictor variable and larger amounts of variability for high values of the predictor variable.
D There should be no pattern in the residual plot.
A penalty kick in soccer involves two players from different teams, the shooter and the goalie. During the penalty kick the shooter will try to score a goal by kicking a soccer ball to the left or right of the goal area. To prevent the shooter from scoring a goal, the goalie will move to the left or right of the goal area. The following table summarizes the directions taken by the shooter and the goalie for 372 penalty kicks. Which of the following indicates an association between the shooter's choice of direction and the goalie's choice of direction? A The marginal relative frequencies for the shooter and the goalie are equal. B The marginal relative frequencies for the shooter and the goalie are not equal. C The row totals are not equal. D For the goalie, the relative frequency of a direction is equal to the relative frequency conditioned on the shooter's direction. E For the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.
E
A researcher collected data on the age, in years, and the growth of sea turtles. The following graph is a residual plot of the regression of growth versus age. Does the residual plot support the appropriateness of a linear model? A Yes, because there is a clear pattern displayed in the residual plot. B Yes, because about half the residuals are positive and the other half are negative. C Yes, because as age increases, the residuals increase. D No, because the points appear to be randomly distributed. E No, because the graph displays a UU-shaped pattern.
E
In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars. Five of the points are labeled A, B, C, D, and E, respectively. Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven? A A B B C C D D E E
E
The least-squares regression line Sˆ=0.5+1.1L models the relationship between the listing price and the actual sales price of 12 houses, with both amounts given in hundred-thousands of dollars. Let L represent the listing price and S represent the sales price. Which of the following is the best interpretation of the slope of the regression line? A. For each hundred-thousand-dollar increase in the listing price, the sales price will increase by $1.1. B. For each hundred-thousand-dollar increase in the listing price, the sales price will increase by $110,000. C. For each hundred-thousand-dollar increase in the listing price, the sales price will decrease by $110,000. D. For each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $1.1. E. or each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $110,000.
For each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $110,000.
